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Rigidity of Einstein four-manifolds with positive sectional curvature
时间  Datetime
 
地点  Venue
报告人  Speaker
Wu, Peng
单位  Affiliation
上海数学中心
邀请人  Host
Lai, Mijia
报告摘要  Abstract
Einstein metrics are most natural Riemannian metrics on differentiable manifolds. In dimensions 2 and 3, they must have constant sectional curvature, while in dimension 4, they are much more complicated. For the complex setting, in 1990 Tian classified Kahler-Einstein four-manifolds with positive scalar curvature, and in 2012 LeBrun classified Hermitian, Einstein four-manifolds with positive scalar curvature. For the real setting, however less is known, even assuming a (strong) condition of positive sectional curvature. In this talk I will first talk about some background on Einstein manifolds, then I will focus on Einstein four-manifolds with positive curvature. If time permitted, I will also talk about my recent attempts of attacking this problem via k-positive curvature operator.